problem_072.js

// This problem was asked by Google.
//
// In a directed graph, each node is assigned an uppercase letter. We define a path's value as the number of most frequently-occurring letter along that path. For example, if a path in the graph goes through "ABACA", the value of the path is 3, since there are 3 occurrences of 'A' on the path.
//
// Given a graph with `n` nodes and `m` directed edges, return the largest value path of the graph. If the largest value is infinite, then return `null`.
//
// The graph is represented with a string and an edge list. The `i`-th character represents the uppercase letter of the `i`-th node. Each tuple in the edge list `(i, j)` means there is a directed edge from the `i`-th node to the `j`-th node. Self-edges are possible, as well as multi-edges.
//
// For example, the following input graph:
//
// `ABACA`
//
// ```
// [(0, 1),
//  (0, 2),
//  (2, 3),
//  (3, 4)]
// ```
//
// Would have maximum value 3 using the path of vertices
//
// `[0, 2, 3, 4]`, `(A, A, C, A)`.
//
// The following input graph:
// `A`
//
// `[(0, 0)]`
//
// Should return null, since we have an infinite loop.